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Adaptive variational quantum eigensolvers (ADAPT-VQEs) are promisingcandidates for simulations of strongly correlated systems on near-term quantumhardware. To further improve the noise resilience of these algorithms, recentefforts have been directed towards compactifying, or layering, their ansatzcircuits. Here, we broaden the understanding of the algorithmic layeringprocess in three ways. First, we investigate the non-commutation relationsbetween the different elements that are used to build ADAPT-VQE ans\"atze.Doing so, we develop a framework for studying and developing layeringalgorithms, which produce shallower circuits. Second, based on this framework,we develop a new subroutine that can reduce the number of quantum-processorcalls by optimizing the selection procedure with which a variational quantumalgorithm appends ansatz elements. Third, we provide a thorough numericalinvestigation of the noise-resilience improvement available via layering thecircuits of ADAPT-VQE algorithms. We find that layering leads to an improvednoise resilience with respect to amplitude-damping and dephasing noise, which,in general, affect idling and non-idling qubits alike. With respect todepolarizing noise, which tends to affect only actively manipulated qubits, weobserve no advantage of layering.

Layering and subpool exploration for adaptive Variational Quantum Eigensolvers: Reducing circuit depth, runtime, and susceptibility to noise